Resolving Entrainment–Mixing in Marine Stratocumulus: The Role of LES Grid Resolution and Super-Droplet Number

Marine stratocumulus clouds profoundly affect Earth’s energy budget by reflecting solar radiation over extensive oceanic areas. Yet, after using a large-eddy simulation (LES) and a Lagrangian microphysics scheme (Super-Droplet Method, SDM) for entrainment-mixing studies, uncertainty remains in the grid resolution and super-droplet number concentration (SDNC) required for accurate homogeneity capture. This study analyzes the homogeneous mixing degree (HMD) and the Damkohler number ($ {\rm{Da}} $) in stratocumulus using an LES with SDM, from microphysical and dynamical perspectives, respectively. Results show that HMD and $ {\rm{Da}} $ both display a top-to-base gradient, with more intense inhomogeneity near the cloud top and relatively homogeneous conditions toward the base, although the upper region is more complex. Even at a fine horizontal resolution of 12.5 m and vertical resolution of 2.5 m, HMD remains sensitive and does not converge, whereas $ {\rm{Da}} $ converges at coarser grid spacings (up to horizontal and vertical spacings of 25 m and 10 m, respectively) in the mid-cloud region. Similarly, HMD requires an SDNC well above 128 per cell for near-complete convergence, while $ {\rm{Da}} $ converges once SDNC exceeds about 16 per cell. This difference arises because HMD depends on microphysical details, thereby demanding a high SDNC to capture local droplet inhomogeneities, whereas $ {\rm{Da}} $ reflects turbulence–evaporation timescales that converge more readily once extreme droplet gradients are resolved. We further find that HMD and $ {\rm{Da}} $ exhibit a significant negative correlation, with stronger anti-correlations emerging under finer spatial resolutions, reinforcing their complementary roles in diagnosing mixing regimes. Overall, these findings provide guidelines for selecting numerical configurations in entrainment–mixing simulations, ensuring that both turbulence-driven and microphysical processes are adequately resolved.